Contractions with rank one defect operators and truncated CMV matrices

The main issue we address in the present paper are the new models for completely nonunitary contractions with rank one defect operators acting on some Hilbert space of dimension N?∞. These models complement nicely the well-known models of Livšic and Sz.-Nagy-Foias. We show that each such operator acting on some finite-dimensional (respectively, separable infinite-dimensional Hilbert space) is unitarily equivalent to some finite (respectively semi-infinite) truncated CMV matrix obtained from the “full” CMV matrix by deleting the first row and the first column, and acting in CN (respectively ?²(N)). This result can be viewed as a nonunitary version of the famous characterization of unitary operators with a simple spectrum due to Cantero, Moral and Velázquez, as well as an analog for contraction operators of the result from [Yu. Arlinski?, E. Tsekanovski?, Non-self-adjoint Jacobi matrices with a rank-one imaginary part, J. Funct. Anal. 241 (2006) 383-438] concerning dissipative non-self-adjoint operators with a rank one imaginary part. It is shown that another functional model for contractions with rank one defect operators takes the form of the compression f(ζ)→PK(ζf(ζ)) on the Hilbert space L²(T,dμ) with a probability measure μ onto the subspace K=L²(T,dμ)?C. The relationship between characteristic functions of sub-matrices of the truncated CMV matrix with rank one defect operators and the corresponding Schur iterates is established. We develop direct and inverse spectral analysis for finite and semi-infinite truncated CMV matrices. In particular, we study the problem of reconstruction of such matrices from their spectrum or the mixed spectral data involving Schur parameters. It is pointed out that if the mixed spectral data contains zero eigenvalue, then no solution, unique solution or infinitely many solutions may occur in the inverse problem for truncated CMV matrices. The uniqueness theorem for recovered truncated CMV matrix from the given mixed spectral data is established. In this part the paper is closely related to the results of Hochstadt and Gesztesy-Simon obtained for finite self-adjoint Jacobi matrices.     

Regular and chaotic precession of magnetization in magnetic films with a stripe domain structure

Based on a numerical solution of the equations of motion found over a wide range of frequencies of an alternating magnetic field, the nonlinear precession dynamics of magnetization are studied in thin-film structures of the (100) type with a stripe domain structure in a perpendicular bias field. The conditions are determined under which high-amplitude regular and chaotic dynamic regimes occur. Bifurcational variations in the precession of coupled magnetic moments and dynamic-bistability states are detected. The specific features of the spectrum of Lyapunov exponents and of time analogs of Poincaré cross sections of trajectories in chaotic regimes are considered.     

Ferrocenylalkyl azoles: bioactivity,synthesis, structure

The toxicity of ferrocenylethyl benzotriazole ( 1 ) and other ferrocene compounds including ferrocenylmethyl benzimidazoles ( 4,5,6,11 ), ferricenium salts ( 3,9,10 ) and ferrocenylmethyl adenine ( 7 ), was studied. All ferrocene complexes under investigation showed low or medium toxicities. On the basis of an earlier model of chemical carcinogenesis, the antitumor activity of ferrocenylalkyl azoles 1, 8 and ferricenium salts 9, 10 was studied in vivo in the so‐called sub‐capsular test on human tumors. This effectiveness was compared with that of cisplatin. A series of ferrocenylalkyl azoles were synthesized by interacting azoles either with α‐hydroxyalkyl ferrocenes FcC(OH)R₁R₂ in organic solvent in the presence of aqueous HBF₄ in quantitative yields or with trimethyl(aminomethyl)ferrocene iodide in an aqueous‐basic medium in good yields. The X‐ray determinations of molecular and crystal structures of α‐(1‐benzotriazolyl)ethylferrocene ( 1 ) and α‐(1‐naphthatriazolyl)ethylferrocene ( 12 ) were performed. Copyright © 2008 John Wiley & Sons, Ltd.     

The measurement of the absorption spectra of chlorine e 6 photosensitizer and hemoglobin in whole blood by multiple light scattering

The potential of using multiple light scattering methods to monitor the state and concentration of photosensitizer and hemoglobin in whole blood is demonstrated. Samples of whole blood with various contents of chlorine e ₆ photosensitizer were studied in the spectral region of 620–850 nm. On the basis of experimentally measured coefficients of diffuse reflection and transmission, absorption spectra of blood with and without the photosensitizer and the concentrations of oxy-, deoxy-, and methemoglobin in the samples are calculated. On the basis of this information, the absorption spectrum of chlorine e ₆ in whole blood is reconstructed and its state and concentration are estimated for the first time. It is found that chlorine e ₆ in whole blood occurs mainly in the monomer form.     

A raman scattering study of the phase transition in the ammonium oxyfluoride (NH4)3TiOF5

Raman spectra of a polycrystalline sample of the perovskite-like oxyfluoride (NH₄)₃TiOF₅ are measured in the frequency region 100–3600 cm^?1 at temperatures ranging from 91 to 370 K under hydrostatic pressures of up to 9 GPa, which include the range of the phase transition from the orientationally disordered cubic phase to the low-symmetry phase. Anomalies in the spectral parameters due to the phase transition are revealed in the range of vibrations of TiOF₅ octahedral groups.     

ML-Based Analysis of Particle Distributions in High-Intensity Laser Experiments: Role of Binning Strategy

When entering the phase of big data processing and statistical inferences in experimental physics, the efficient use of machine learning methods may require optimal data preprocessing methods and, in particular, optimal balance between details and noise. In experimental studies of strong-field quantum electrodynamics with intense lasers, this balance concerns data binning for the observed distributions of particles and photons. Here we analyze the aspect of binning with respect to different machine learning methods (Support Vector Machine (SVM), Gradient Boosting Trees (GBT), Fully-Connected Neural Network (FCNN), Convolutional Neural Network (CNN)) using numerical simulations that mimic expected properties of upcoming experiments. We see that binning can crucially affect the performance of SVM and GBT, and, to a less extent, FCNN and CNN. This can be interpreted as the latter methods being able to effectively learn the optimal binning, discarding unnecessary information. Nevertheless, given limited training sets, the results indicate that the efficiency can be increased by optimizing the binning scale along with other hyperparameters. We present specific measurements of accuracy that can be useful for planning of experiments in the specified research area.     

Hydrodynamic formation of stable anisotropic structures in Couette flow of dilute suspensionFormation hydrodynamique pour structures anisotropiques stables dans un flux de Couette d'une suspension diluée

The problem of rotary motion of rigid axially symmetric elongated particles in the Couette flow of dilute suspension with anisotropic carrier fluid is solved. It is shown that the stable stationary solutions of the dynamical set of ordinary differential equations describing the particles rotary motion are possible in the case of forming the stationary anisotropy in the carrier fluid of the suspension. It allows us to detect the stationary orientation of suspended particles and formation of stable anisotropic liquid-crystalline structures in the considered suspension under the action of hydrodynamic forces. The study of rheological properties of such a structured suspension shows that it behaves as a viscoelastic quasi-Newtonian anisotropic liquid medium. To cite this article: E.Yu. Taran et al., C. R. Mecanique 332 (2004).     

Lewis acid catalyzed reactions of donor-acceptor cyclopropanes with 1- and 2-pyrazolines: formation of substituted 2-pyrazolines and 1,2-diazabicyclo[3.3.0]octanes

The reaction of 2-substituted cyclopropane-1,1-dicarboxylates with 1- and 2-pyrazolines is efficiently catalyzed by scandium or ytterbium triflates to give N-substituted 2-pyrazolines or 1,2-diazabicyclo[3.3.0]octanes. The reactions of 2-pyrazolines give diazabicyclooctanes as the major products. In contrast, the reactions starting from 1-pyrazolines predominantly give N-substituted 2-pyrazolines, which become the major compounds obtained if an equimolar amount of GaCl₃ is used. A possible reaction mechanism is suggested.     

Impact of synthesis conditions on surface chemistry and structure of carbide-derived carbons

Carbide-derived carbons produced by chlorination of titanium carbide at 600, 800, or 1100 °C were subjected to a post-treatment at 600 °C in Ar, H₂, or NH₃ atmosphere. Experimental results suggest that the chlorination temperature influences the ordering of carbon in a manner that impacts specific surface area and porosity. Higher chlorination temperatures lead to higher total pore volume and increased ordering, but lower microporosity. The effect of post-treatments on surface chemistry is pronounced only for samples chlorinated at 600 °C; post-treatments in Ar are shown to be less effective for chlorine removal than those performed in H₂ or NH₃. Post-treatments in Ar result in a lower total pore volume compared to the ones in H₂ or NH₃ for the same chlorination temperature. Samples chlorinated at higher temperatures contained less oxygen functionalities than samples chlorinated at 600 °C, and showed correspondingly less desorption of H₂O, possibly due to diminished uptake of ambient water.